Loho, Georg PeterSchymura, Matthias2019-08-222019-08-222019-08-222019-08-22https://infoscience.epfl.ch/handle/20.500.14299/1600911908.07893We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposition is complemented by a brief study of arising complexity questions.text::preprint